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McGuire
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The following is a question regarding the derivation of Einstein's field equations.
Background
In deriving his equations, it is my understanding that Einstein equated the Einstein Tensor Gμv and the Cosmological Constant*Metric Tensor with the Stress Energy Momentum Tensor Tμv term simply because the covariant derivative of all three terms equals zero.
Rμv - (1/2)*gμv*R + [itex]\Lambda[/itex]*gμv = (8*pi*G)/(c4)*Tμv
Question
Is this basis for equivalence (that terms are equivalent if their covariant derivatives are equal) standard practice in mathematics, or did Einstein take a leap of faith?
Thank you very much for your time! Please let me know if I can clarify my question.
Background
In deriving his equations, it is my understanding that Einstein equated the Einstein Tensor Gμv and the Cosmological Constant*Metric Tensor with the Stress Energy Momentum Tensor Tμv term simply because the covariant derivative of all three terms equals zero.
Rμv - (1/2)*gμv*R + [itex]\Lambda[/itex]*gμv = (8*pi*G)/(c4)*Tμv
Question
Is this basis for equivalence (that terms are equivalent if their covariant derivatives are equal) standard practice in mathematics, or did Einstein take a leap of faith?
Thank you very much for your time! Please let me know if I can clarify my question.
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